LMFDB - Embedded newform 729.2.e.k.325.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 $ x^12 + 18x^10 + 105x^8 + 266x^6 + 306x^4 + 132*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			325.1
Root			$-1.13697i$ of defining polynomial
Character	$\chi$	$=$	729.325
Dual form			729.2.e.k.406.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.595778 + 0.499917i) q^{2} +(-0.242262 + 1.37394i) q^{4} +(2.23304 - 0.812759i) q^{5} +(-0.434359 - 2.46337i) q^{7} +(-1.32025 - 2.28674i) q^{8} +O(q^{10})$	\(q+(-0.595778 + 0.499917i) q^{2} +(-0.242262 + 1.37394i) q^{4} +(2.23304 - 0.812759i) q^{5} +(-0.434359 - 2.46337i) q^{7} +(-1.32025 - 2.28674i) q^{8} +(-0.924081 + 1.60056i) q^{10} +(2.95192 + 1.07441i) q^{11} +(1.02392 + 0.859169i) q^{13} +(1.49026 + 1.25048i) q^{14} +(-0.692233 - 0.251952i) q^{16} +(3.13726 - 5.43389i) q^{17} +(-4.03234 - 6.98422i) q^{19} +(0.575699 + 3.26495i) q^{20} +(-2.29581 + 0.835605i) q^{22} +(-0.704074 + 3.99300i) q^{23} +(0.495652 - 0.415902i) q^{25} -1.03954 q^{26} +3.48975 q^{28} +(7.11443 - 5.96971i) q^{29} +(0.491741 - 2.78880i) q^{31} +(5.50090 - 2.00216i) q^{32} +(0.847385 + 4.80576i) q^{34} +(-2.97207 - 5.14778i) q^{35} +(-2.76596 + 4.79078i) q^{37} +(5.89391 + 2.14521i) q^{38} +(-4.80674 - 4.03334i) q^{40} +(5.44333 + 4.56750i) q^{41} +(-2.19597 - 0.799267i) q^{43} +(-2.19131 + 3.79547i) q^{44} +(-1.57670 - 2.73092i) q^{46} +(0.801248 + 4.54411i) q^{47} +(0.698301 - 0.254161i) q^{49} +(-0.0873823 + 0.495570i) q^{50} +(-1.42850 + 1.19865i) q^{52} -0.135496 q^{53} +7.46499 q^{55} +(-5.05964 + 4.24554i) q^{56} +(-1.25426 + 7.11324i) q^{58} +(-3.75759 + 1.36765i) q^{59} +(0.0593526 + 0.336605i) q^{61} +(1.10120 + 1.90733i) q^{62} +(-1.53974 + 2.66690i) q^{64} +(2.98474 + 1.08636i) q^{65} +(7.75461 + 6.50689i) q^{67} +(6.70579 + 5.62682i) q^{68} +(4.34415 + 1.58114i) q^{70} +(4.09540 - 7.09344i) q^{71} +(6.15722 + 10.6646i) q^{73} +(-0.747095 - 4.23698i) q^{74} +(10.5728 - 3.84817i) q^{76} +(1.36448 - 7.73837i) q^{77} +(3.12600 - 2.62302i) q^{79} -1.75056 q^{80} -5.52638 q^{82} +(-0.699573 + 0.587012i) q^{83} +(2.58917 - 14.6839i) q^{85} +(1.70788 - 0.621616i) q^{86} +(-1.44038 - 8.16879i) q^{88} +(-1.86437 - 3.22919i) q^{89} +(1.67171 - 2.89548i) q^{91} +(-5.31556 - 1.93471i) q^{92} +(-2.74904 - 2.30672i) q^{94} +(-14.6809 - 12.3187i) q^{95} +(5.63467 + 2.05085i) q^{97} +(-0.288973 + 0.500515i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 6 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 6 * q^7 - 6 * q^8	$ 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 6 q^{10} + 15 q^{11} - 3 q^{13} + 21 q^{14} + 9 q^{16} + 9 q^{17} - 12 q^{19} + 3 q^{20} + 33 q^{22} - 15 q^{23} - 12 q^{25} + 48 q^{26} + 6 q^{28} + 6 q^{29} - 12 q^{31} + 27 q^{32} + 27 q^{34} - 30 q^{35} - 3 q^{37} + 39 q^{38} + 24 q^{40} + 39 q^{41} + 24 q^{43} + 33 q^{44} + 3 q^{46} + 42 q^{47} - 30 q^{49} + 15 q^{50} - 45 q^{52} - 18 q^{53} + 30 q^{55} - 12 q^{56} - 30 q^{58} - 15 q^{59} - 3 q^{61} + 30 q^{62} - 6 q^{64} + 6 q^{65} - 3 q^{67} - 36 q^{68} - 75 q^{70} - 12 q^{73} - 60 q^{74} + 30 q^{76} - 33 q^{77} + 33 q^{79} - 42 q^{80} - 42 q^{82} + 33 q^{83} - 18 q^{85} + 30 q^{86} - 42 q^{88} + 9 q^{89} - 18 q^{91} - 33 q^{92} - 66 q^{94} - 12 q^{95} + 15 q^{97} - 18 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 6 * q^10 + 15 * q^11 - 3 * q^13 + 21 * q^14 + 9 * q^16 + 9 * q^17 - 12 * q^19 + 3 * q^20 + 33 * q^22 - 15 * q^23 - 12 * q^25 + 48 * q^26 + 6 * q^28 + 6 * q^29 - 12 * q^31 + 27 * q^32 + 27 * q^34 - 30 * q^35 - 3 * q^37 + 39 * q^38 + 24 * q^40 + 39 * q^41 + 24 * q^43 + 33 * q^44 + 3 * q^46 + 42 * q^47 - 30 * q^49 + 15 * q^50 - 45 * q^52 - 18 * q^53 + 30 * q^55 - 12 * q^56 - 30 * q^58 - 15 * q^59 - 3 * q^61 + 30 * q^62 - 6 * q^64 + 6 * q^65 - 3 * q^67 - 36 * q^68 - 75 * q^70 - 12 * q^73 - 60 * q^74 + 30 * q^76 - 33 * q^77 + 33 * q^79 - 42 * q^80 - 42 * q^82 + 33 * q^83 - 18 * q^85 + 30 * q^86 - 42 * q^88 + 9 * q^89 - 18 * q^91 - 33 * q^92 - 66 * q^94 - 12 * q^95 + 15 * q^97 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.595778	+	0.499917i	−0.421278	+	0.353495i	−0.828649	−	0.559768i	$-0.810890\pi$
$2$	−0.595778	+	0.499917i	−0.421278	+	0.353495i	0.407371	+	0.913263i	$0.366446\pi$
$3$		0			0
$3$		0			0
$4$	−0.242262	+	1.37394i	−0.121131	+	0.686969i
$5$	2.23304	−	0.812759i	0.998644	−	0.363477i	0.209583	−	0.977791i	$-0.432789\pi$
$5$	2.23304	−	0.812759i	0.998644	−	0.363477i	0.789062	+	0.614314i	$0.210567\pi$
$6$		0			0
$7$	−0.434359	−	2.46337i	−0.164172	−	0.931068i	−0.949914	−	0.312513i	$-0.898829\pi$
$7$	−0.434359	−	2.46337i	−0.164172	−	0.931068i	0.785741	−	0.618555i	$-0.212282\pi$
$8$	−1.32025	−	2.28674i	−0.466780	−	0.808486i
$9$		0			0
$10$	−0.924081	+	1.60056i	−0.292220	+	0.506140i
$11$	2.95192	+	1.07441i	0.890038	+	0.323947i	0.746254	−	0.665662i	$-0.231851\pi$
$11$	2.95192	+	1.07441i	0.890038	+	0.323947i	0.143784	+	0.989609i	$0.454073\pi$
$12$		0			0
$13$	1.02392	+	0.859169i	0.283984	+	0.238291i	0.773641	−	0.633624i	$-0.218434\pi$
$13$	1.02392	+	0.859169i	0.283984	+	0.238291i	−0.489657	+	0.871915i	$0.662878\pi$
$14$	1.49026	+	1.25048i	0.398290	+	0.334205i
$15$		0			0
$16$	−0.692233	−	0.251952i	−0.173058	−	0.0629881i
$17$	3.13726	−	5.43389i	0.760897	−	1.31791i	−0.181492	−	0.983392i	$-0.558093\pi$
$17$	3.13726	−	5.43389i	0.760897	−	1.31791i	0.942389	−	0.334520i	$-0.108574\pi$
$18$		0			0
$19$	−4.03234	−	6.98422i	−0.925083	−	1.60229i	−0.791427	−	0.611263i	$-0.790662\pi$
$19$	−4.03234	−	6.98422i	−0.925083	−	1.60229i	−0.133656	−	0.991028i	$-0.542672\pi$
$20$	0.575699	+	3.26495i	0.128730	+	0.730066i
$21$		0			0
$22$	−2.29581	+	0.835605i	−0.489467	+	0.178152i
$23$	−0.704074	+	3.99300i	−0.146810	+	0.832598i	0.819087	+	0.573669i	$0.194481\pi$
$23$	−0.704074	+	3.99300i	−0.146810	+	0.832598i	−0.965896	+	0.258929i	$0.916631\pi$
$24$		0			0
$25$	0.495652	−	0.415902i	0.0991305	−	0.0831803i
$26$	−1.03954			−0.203871
$27$		0			0
$28$	3.48975			0.659501
$29$	7.11443	−	5.96971i	1.32112	−	1.10855i	0.335049	−	0.942201i	$-0.391247\pi$
$29$	7.11443	−	5.96971i	1.32112	−	1.10855i	0.986067	−	0.166347i	$-0.0531973\pi$
$30$		0			0
$31$	0.491741	−	2.78880i	0.0883192	−	0.500883i	−0.908272	−	0.418381i	$-0.862598\pi$
$31$	0.491741	−	2.78880i	0.0883192	−	0.500883i	0.996591	−	0.0825022i	$-0.0262912\pi$
$32$	5.50090	−	2.00216i	0.972430	−	0.353936i
$33$		0			0
$34$	0.847385	+	4.80576i	0.145325	+	0.824181i
$35$	−2.97207	−	5.14778i	−0.502372	−	0.870133i
$36$		0			0
$37$	−2.76596	+	4.79078i	−0.454720	+	0.787599i	−0.998672	−	0.0515178i	$-0.983594\pi$
$37$	−2.76596	+	4.79078i	−0.454720	+	0.787599i	0.543952	+	0.839117i	$0.316927\pi$
$38$	5.89391	+	2.14521i	0.956119	+	0.347999i
$39$		0			0
$40$	−4.80674	−	4.03334i	−0.760013	−	0.637726i
$41$	5.44333	+	4.56750i	0.850105	+	0.713323i	0.959813	−	0.280641i	$-0.0905470\pi$
$41$	5.44333	+	4.56750i	0.850105	+	0.713323i	−0.109708	+	0.993964i	$0.534991\pi$
$42$		0			0
$43$	−2.19597	−	0.799267i	−0.334882	−	0.121887i	0.169106	−	0.985598i	$-0.445912\pi$
$43$	−2.19597	−	0.799267i	−0.334882	−	0.121887i	−0.503988	+	0.863711i	$0.668134\pi$
$44$	−2.19131	+	3.79547i	−0.330353	+	0.572188i
$45$		0			0
$46$	−1.57670	−	2.73092i	−0.232471	−	0.402652i
$47$	0.801248	+	4.54411i	0.116874	+	0.662826i	0.985805	+	0.167893i	$0.0536963\pi$
$47$	0.801248	+	4.54411i	0.116874	+	0.662826i	−0.868931	+	0.494933i	$0.835193\pi$
$48$		0			0
$49$	0.698301	−	0.254161i	0.0997573	−	0.0363087i
$50$	−0.0873823	+	0.495570i	−0.0123577	+	0.0700842i
$51$		0			0
$52$	−1.42850	+	1.19865i	−0.198097	+	0.166224i
$53$	−0.135496			−0.0186118			−0.00930588	−	0.999957i	$-0.502962\pi$
$53$	−0.135496			−0.0186118			−0.00930588	+	0.999957i	$0.502962\pi$
$54$		0			0
$55$	7.46499			1.00658
$56$	−5.05964	+	4.24554i	−0.676123	+	0.567335i
$57$		0			0
$58$	−1.25426	+	7.11324i	−0.164692	+	0.934015i
$59$	−3.75759	+	1.36765i	−0.489196	+	0.178053i	−0.574828	−	0.818274i	$-0.694931\pi$
$59$	−3.75759	+	1.36765i	−0.489196	+	0.178053i	0.0856324	+	0.996327i	$0.472709\pi$
$60$		0			0
$61$	0.0593526	+	0.336605i	0.00759932	+	0.0430979i	0.988372	−	0.152058i	$-0.0485899\pi$
$61$	0.0593526	+	0.336605i	0.00759932	+	0.0430979i	−0.980772	+	0.195156i	$0.937479\pi$
$62$	1.10120	+	1.90733i	0.139852	+	0.242232i
$63$		0			0
$64$	−1.53974	+	2.66690i	−0.192467	+	0.333363i
$65$	2.98474	+	1.08636i	0.370212	+	0.134746i
$66$		0			0
$67$	7.75461	+	6.50689i	0.947376	+	0.794943i	0.978854	−	0.204562i	$-0.0655769\pi$
$67$	7.75461	+	6.50689i	0.947376	+	0.794943i	−0.0314778	+	0.999504i	$0.510021\pi$
$68$	6.70579	+	5.62682i	0.813196	+	0.682353i
$69$		0			0
$70$	4.34415	+	1.58114i	0.519225	+	0.188983i
$71$	4.09540	−	7.09344i	0.486035	−	0.841837i	−0.513837	−	0.857888i	$-0.671776\pi$
$71$	4.09540	−	7.09344i	0.486035	−	0.841837i	0.999871	+	0.0160515i	$0.00510955\pi$
$72$		0			0
$73$	6.15722	+	10.6646i	0.720648	+	1.24820i	0.960740	+	0.277449i	$0.0894890\pi$
$73$	6.15722	+	10.6646i	0.720648	+	1.24820i	−0.240092	+	0.970750i	$0.577178\pi$
$74$	−0.747095	−	4.23698i	−0.0868480	−	0.492539i
$75$		0			0
$76$	10.5728	−	3.84817i	1.21278	−	0.441416i
$77$	1.36448	−	7.73837i	0.155497	−	0.881869i
$78$		0			0
$79$	3.12600	−	2.62302i	0.351702	−	0.295113i	−0.449771	−	0.893144i	$-0.648494\pi$
$79$	3.12600	−	2.62302i	0.351702	−	0.295113i	0.801473	+	0.598031i	$0.204050\pi$
$80$	−1.75056			−0.195718
$81$		0			0
$82$	−5.52638			−0.610287
$83$	−0.699573	+	0.587012i	−0.0767881	+	0.0644329i	−0.680374	−	0.732865i	$-0.738183\pi$
$83$	−0.699573	+	0.587012i	−0.0767881	+	0.0644329i	0.603586	+	0.797298i	$0.293738\pi$
$84$		0			0
$85$	2.58917	−	14.6839i	0.280835	−	1.59269i
$86$	1.70788	−	0.621616i	0.184165	−	0.0670306i
$87$		0			0
$88$	−1.44038	−	8.16879i	−0.153545	−	0.870795i
$89$	−1.86437	−	3.22919i	−0.197623	−	0.342293i	0.750134	−	0.661286i	$-0.229989\pi$
$89$	−1.86437	−	3.22919i	−0.197623	−	0.342293i	−0.947757	+	0.318992i	$0.896656\pi$
$90$		0			0
$91$	1.67171	−	2.89548i	0.175243	−	0.303529i
$92$	−5.31556	−	1.93471i	−0.554186	−	0.201707i
$93$		0			0
$94$	−2.74904	−	2.30672i	−0.283542	−	0.237920i
$95$	−14.6809	−	12.3187i	−1.50622	−	1.26387i
$96$		0			0
$97$	5.63467	+	2.05085i	0.572115	+	0.208233i	0.611845	−	0.790978i	$-0.290428\pi$
$97$	5.63467	+	2.05085i	0.572115	+	0.208233i	−0.0397303	+	0.999210i	$0.512650\pi$
$98$	−0.288973	+	0.500515i	−0.0291907	+	0.0505597i
$99$		0			0
$100$	0.451345	+	0.781752i	0.0451345	+	0.0781752i
$101$	−1.77498	−	10.0664i	−0.176617	−	1.00165i	−0.936261	−	0.351306i	$-0.885738\pi$
$101$	−1.77498	−	10.0664i	−0.176617	−	1.00165i	0.759643	−	0.650340i	$-0.225374\pi$
$102$		0			0
$103$	−8.01939	+	2.91882i	−0.790174	+	0.287600i	−0.705409	−	0.708801i	$-0.749236\pi$
$103$	−8.01939	+	2.91882i	−0.790174	+	0.287600i	−0.0847658	+	0.996401i	$0.527014\pi$
$104$	0.612870	−	3.47576i	0.0600968	−	0.340826i
$105$		0			0
$106$	0.0807253	−	0.0677366i	0.00784073	−	0.00657916i
$107$	7.74500			0.748738			0.374369	−	0.927280i	$-0.377859\pi$
$107$	7.74500			0.748738			0.374369	+	0.927280i	$0.377859\pi$
$108$		0			0
$109$	1.25438			0.120148			0.0600738	−	0.998194i	$-0.480866\pi$
$109$	1.25438			0.120148			0.0600738	+	0.998194i	$0.480866\pi$
$110$	−4.44747	+	3.73187i	−0.424050	+	0.355820i
$111$		0			0
$112$	−0.319975	+	1.81467i	−0.0302348	+	0.171470i
$113$	−16.6897	+	6.07454i	−1.57003	+	0.571445i	−0.973006	−	0.230778i	$-0.925873\pi$
$113$	−16.6897	+	6.07454i	−1.57003	+	0.571445i	−0.597025	+	0.802223i	$0.703651\pi$
$114$		0			0
$115$	1.67312	+	9.48876i	0.156020	+	0.884831i
$116$	6.47846	+	11.2210i	0.601509	+	1.04185i
$117$		0			0
$118$	1.55497	−	2.69329i	0.143147	−	0.247938i
$119$	−14.7484	−	5.36798i	−1.35198	−	0.492082i
$120$		0			0
$121$	−0.867002	−	0.727501i	−0.0788184	−	0.0661365i
$122$	−0.203636	−	0.170871i	−0.0184363	−	0.0154699i
$123$		0			0
$124$	3.71250	+	1.35124i	0.333393	+	0.121345i
$125$	−5.17209	+	8.95832i	−0.462606	+	0.801256i
$126$		0			0
$127$	1.98279	+	3.43429i	0.175944	+	0.304744i	0.940488	−	0.339828i	$-0.110369\pi$
$127$	1.98279	+	3.43429i	0.175944	+	0.304744i	−0.764543	+	0.644572i	$0.777036\pi$
$128$	1.61716	+	9.17137i	0.142938	+	0.810643i
$129$		0			0
$130$	−2.32133	+	0.844896i	−0.203594	+	0.0741022i
$131$	0.0177987	−	0.100941i	0.00155508	−	0.00881927i	−0.984020	−	0.178056i	$-0.943019\pi$
$131$	0.0177987	−	0.100941i	0.00155508	−	0.00881927i	0.985575	+	0.169237i	$0.0541303\pi$
$132$		0			0
$133$	−15.4533	+	12.9668i	−1.33997	+	1.12437i
$134$	−7.87292			−0.680117
$135$		0			0
$136$	−16.5679			−1.42068
$137$	5.83691	−	4.89775i	0.498681	−	0.418443i	−0.358444	−	0.933551i	$-0.616693\pi$
$137$	5.83691	−	4.89775i	0.498681	−	0.418443i	0.857125	+	0.515108i	$0.172248\pi$
$138$		0			0
$139$	−1.81301	+	10.2821i	−0.153778	+	0.872117i	0.806117	+	0.591756i	$0.201565\pi$
$139$	−1.81301	+	10.2821i	−0.153778	+	0.872117i	−0.959895	+	0.280361i	$0.909546\pi$
$140$	7.79274	−	2.83633i	0.658607	−	0.239713i
$141$		0			0
$142$	1.10618	+	6.27347i	0.0928288	+	0.526458i
$143$	2.09943	+	3.63631i	0.175563	+	0.304084i
$144$		0			0
$145$	11.0348	−	19.1129i	0.916394	−	1.58724i
$146$	−8.99975	−	3.27564i	−0.744825	−	0.271094i
$147$		0			0
$148$	−5.91214	−	4.96087i	−0.485975	−	0.407781i
$149$	−6.91936	−	5.80603i	−0.566856	−	0.475648i	0.313745	−	0.949507i	$-0.398416\pi$
$149$	−6.91936	−	5.80603i	−0.566856	−	0.475648i	−0.880601	+	0.473859i	$0.842861\pi$
$150$		0			0
$151$	−22.4496	−	8.17099i	−1.82692	−	0.664946i	−0.993708	−	0.111998i	$-0.964275\pi$
$151$	−22.4496	−	8.17099i	−1.82692	−	0.664946i	−0.833216	−	0.552948i	$-0.813503\pi$
$152$	−10.6474	+	18.4419i	−0.863620	+	1.49583i
$153$		0			0
$154$	3.05561	+	5.29248i	0.246228	+	0.426480i
$155$	−1.16855	−	6.62716i	−0.0938599	−	0.532306i
$156$		0			0
$157$	−2.54843	+	0.927554i	−0.203387	+	0.0740269i	−0.441705	−	0.897160i	$-0.645626\pi$
$157$	−2.54843	+	0.927554i	−0.203387	+	0.0740269i	0.238318	+	0.971187i	$0.423404\pi$
$158$	−0.551105	+	3.12547i	−0.0438436	+	0.248649i
$159$		0			0
$160$	10.6564	−	8.94180i	0.842465	−	0.706912i
$161$	10.1421			0.799308
$162$		0			0
$163$	−22.0489			−1.72701			−0.863504	−	0.504343i	$-0.831735\pi$
$163$	−22.0489			−1.72701			−0.863504	+	0.504343i	$0.831735\pi$
$164$	−7.59416	+	6.37226i	−0.593005	+	0.497590i
$165$		0			0
$166$	0.123333	−	0.699457i	0.00957251	−	0.0542884i
$167$	−8.41101	+	3.06136i	−0.650863	+	0.236895i	−0.646287	−	0.763095i	$-0.723679\pi$
$167$	−8.41101	+	3.06136i	−0.650863	+	0.236895i	−0.00457649	+	0.999990i	$0.501457\pi$
$168$		0			0
$169$	−1.94719	−	11.0431i	−0.149784	−	0.849466i
$170$	5.79816	+	10.0427i	0.444699	+	0.770241i
$171$		0			0
$172$	1.63014	−	2.82349i	0.124297	−	0.215289i
$173$	−2.47538	−	0.900966i	−0.188200	−	0.0684992i	0.246201	−	0.969219i	$-0.420818\pi$
$173$	−2.47538	−	0.900966i	−0.188200	−	0.0684992i	−0.434401	+	0.900720i	$0.643040\pi$
$174$		0			0
$175$	−1.23981	−	1.04033i	−0.0937211	−	0.0786413i
$176$	−1.77272	−	1.48749i	−0.133624	−	0.112124i
$177$		0			0
$178$	2.72508	+	0.991847i	0.204253	+	0.0743421i
$179$	−1.84227	+	3.19090i	−0.137697	+	0.238499i	−0.926625	−	0.375988i	$-0.877303\pi$
$179$	−1.84227	+	3.19090i	−0.137697	+	0.238499i	0.788927	+	0.614487i	$0.210637\pi$
$180$		0			0
$181$	0.134255	+	0.232536i	0.00997906	+	0.0172842i	0.870972	−	0.491333i	$-0.163490\pi$
$181$	0.134255	+	0.232536i	0.00997906	+	0.0172842i	−0.860993	+	0.508617i	$0.830157\pi$
$182$	0.451534	+	2.56078i	0.0334699	+	0.189817i
$183$		0			0
$184$	10.0605	−	3.66173i	0.741672	−	0.269946i
$185$	−2.28273	+	12.9460i	−0.167830	+	0.951811i
$186$		0			0
$187$	15.0992	−	12.6697i	1.10416	−	0.926502i
$188$	−6.43743			−0.469498
$189$		0			0
$190$	14.9049			1.08131
$191$	−1.83696	+	1.54140i	−0.132918	+	0.111531i	−0.706823	−	0.707390i	$-0.749872\pi$
$191$	−1.83696	+	1.54140i	−0.132918	+	0.111531i	0.573905	+	0.818922i	$0.305428\pi$
$192$		0			0
$193$	0.0861647	−	0.488664i	0.00620227	−	0.0351748i	−0.981550	−	0.191208i	$-0.938760\pi$
$193$	0.0861647	−	0.488664i	0.00620227	−	0.0351748i	0.987752	+	0.156033i	$0.0498706\pi$
$194$	−4.38227	+	1.59502i	−0.314629	+	0.114515i
$195$		0			0
$196$	0.180029	+	1.02099i	0.0128592	+	0.0729282i
$197$	11.0734	+	19.1797i	0.788946	+	1.36649i	0.926613	+	0.376016i	$0.122706\pi$
$197$	11.0734	+	19.1797i	0.788946	+	1.36649i	−0.137667	+	0.990479i	$0.543960\pi$
$198$		0			0
$199$	−1.06624	+	1.84677i	−0.0755834	+	0.130914i	−0.901340	−	0.433113i	$-0.857415\pi$
$199$	−1.06624	+	1.84677i	−0.0755834	+	0.130914i	0.825756	+	0.564027i	$0.190749\pi$
$200$	−1.60545	−	0.584335i	−0.113522	−	0.0413187i
$201$		0			0
$202$	6.08987	+	5.11001i	0.428482	+	0.359539i
$203$	−17.7959	−	14.9325i	−1.24902	−	1.04806i
$204$		0			0
$205$	15.8674	+	5.77527i	1.10823	+	0.403362i
$206$	3.31861	−	5.74800i	0.231218	−	0.400482i
$207$		0			0
$208$	−0.492320	−	0.852724i	−0.0341363	−	0.0591257i
$209$	−4.39923	−	24.9493i	−0.304301	−	1.72578i
$210$		0			0
$211$	−18.8019	+	6.84334i	−1.29438	+	0.471115i	−0.895162	−	0.445742i	$-0.852940\pi$
$211$	−18.8019	+	6.84334i	−1.29438	+	0.471115i	−0.399216	+	0.916857i	$0.630718\pi$
$212$	0.0328255	−	0.186163i	0.00225446	−	0.0127857i
$213$		0			0
$214$	−4.61430	+	3.87186i	−0.315427	+	0.264675i
$215$	−5.55329			−0.378731
$216$		0			0
$217$	−7.08345			−0.480856
$218$	−0.747330	+	0.627084i	−0.0506156	+	0.0424715i
$219$		0			0
$220$	−1.80848	+	10.2564i	−0.121928	+	0.691488i
$221$	7.88093	−	2.86842i	0.530129	−	0.192951i
$222$		0			0
$223$	−2.30578	−	13.0767i	−0.154407	−	0.875683i	−0.959326	−	0.282299i	$-0.908903\pi$
$223$	−2.30578	−	13.0767i	−0.154407	−	0.875683i	0.804920	−	0.593384i	$-0.202208\pi$
$224$	−7.32144	−	12.6811i	−0.489185	−	0.847292i
$225$		0			0
$226$	6.90656	−	11.9625i	0.459418	−	0.795735i
$227$	11.7188	+	4.26531i	0.777807	+	0.283099i	0.700258	−	0.713890i	$-0.253068\pi$
$227$	11.7188	+	4.26531i	0.777807	+	0.283099i	0.0775490	+	0.996989i	$0.475291\pi$
$228$		0			0
$229$	19.6579	+	16.4949i	1.29903	+	1.09002i	0.990312	+	0.138862i	$0.0443445\pi$
$229$	19.6579	+	16.4949i	1.29903	+	1.09002i	0.308719	+	0.951153i	$0.400100\pi$
$230$	−5.74040	−	4.81677i	−0.378511	−	0.317608i
$231$		0			0
$232$	−23.0440	−	8.38735i	−1.51292	−	0.550656i
$233$	2.69821	−	4.67344i	0.176766	−	0.306167i	−0.764005	−	0.645210i	$-0.776770\pi$
$233$	2.69821	−	4.67344i	0.176766	−	0.306167i	0.940771	+	0.339043i	$0.110103\pi$
$234$		0			0
$235$	5.48248	+	9.49593i	0.357637	+	0.619446i
$236$	−0.968743	−	5.49402i	−0.0630598	−	0.357630i
$237$		0			0
$238$	11.4703	−	4.17485i	0.743510	−	0.270616i
$239$	1.45362	−	8.24387i	0.0940266	−	0.533252i	−0.901015	−	0.433789i	$-0.857176\pi$
$239$	1.45362	−	8.24387i	0.0940266	−	0.533252i	0.995041	−	0.0994629i	$-0.0317124\pi$
$240$		0			0
$241$	−0.338737	+	0.284234i	−0.0218200	+	0.0183091i	−0.653632	−	0.756812i	$-0.726756\pi$
$241$	−0.338737	+	0.284234i	−0.0218200	+	0.0183091i	0.631812	+	0.775121i	$0.282311\pi$
$242$	0.880231			0.0565834
$243$		0			0
$244$	−0.476854			−0.0305274
$245$	1.35276	−	1.13510i	0.0864246	−	0.0725189i
$246$		0			0
$247$	1.87184	−	10.6157i	0.119102	−	0.675463i
$248$	−7.02649	+	2.55743i	−0.446183	+	0.162397i
$249$		0			0
$250$	−1.39700	−	7.92278i	−0.0883540	−	0.501080i
$251$	−8.51427	−	14.7471i	−0.537416	−	0.930832i	−0.999042	−	0.0437571i	$-0.986067\pi$
$251$	−8.51427	−	14.7471i	−0.537416	−	0.930832i	0.461626	−	0.887074i	$-0.347266\pi$
$252$		0			0
$253$	−6.36850	+	11.0306i	−0.400384	+	0.693486i
$254$	−2.89816	−	1.05484i	−0.181847	−	0.0661869i
$255$		0			0
$256$	−10.2664	−	8.61455i	−0.641651	−	0.538409i
$257$	15.9925	+	13.4193i	0.997584	+	0.837073i	0.986648	−	0.162867i	$-0.0520743\pi$
$257$	15.9925	+	13.4193i	0.997584	+	0.837073i	0.0109365	+	0.999940i	$0.496519\pi$
$258$		0			0
$259$	13.0029	+	4.73267i	0.807961	+	0.294074i
$260$	−2.21568	+	3.83767i	−0.137411	+	0.238002i
$261$		0			0
$262$	0.0398582	+	0.0690364i	0.00246245	+	0.00426508i
$263$	3.36731	+	19.0970i	0.207637	+	1.17757i	0.893236	+	0.449589i	$0.148429\pi$
$263$	3.36731	+	19.0970i	0.207637	+	1.17757i	−0.685599	+	0.727980i	$0.740459\pi$
$264$		0			0
$265$	−0.302567	+	0.110125i	−0.0185865	+	0.00676495i
$266$	2.72438	−	15.4507i	0.167042	−	0.947343i
$267$		0			0
$268$	−10.8187	+	9.07797i	−0.660857	+	0.554525i
$269$	18.6791			1.13889			0.569443	−	0.822031i	$-0.307159\pi$
$269$	18.6791			1.13889			0.569443	+	0.822031i	$0.307159\pi$
$270$		0			0
$271$	12.9378			0.785917			0.392958	−	0.919556i	$-0.371452\pi$
$271$	12.9378			0.785917			0.392958	+	0.919556i	$0.371452\pi$
$272$	−3.54080	+	2.97108i	−0.214692	+	0.180148i
$273$		0			0
$274$	−1.02903	+	5.83594i	−0.0621662	+	0.352562i
$275$	1.90998	−	0.695175i	0.115176	−	0.0419206i
$276$		0			0
$277$	1.81312	+	10.2827i	0.108940	+	0.617828i	0.989573	+	0.144030i	$0.0460061\pi$
$277$	1.81312	+	10.2827i	0.108940	+	0.617828i	−0.880634	+	0.473798i	$0.842883\pi$
$278$	−4.06005	−	7.03221i	−0.243505	−	0.421764i
$279$		0			0
$280$	−7.84776	+	13.5927i	−0.468994	+	0.812321i
$281$	−13.4806	−	4.90655i	−0.804187	−	0.292700i	−0.0929668	−	0.995669i	$-0.529635\pi$
$281$	−13.4806	−	4.90655i	−0.804187	−	0.292700i	−0.711221	+	0.702969i	$0.751857\pi$
$282$		0			0
$283$	−14.3194	−	12.0154i	−0.851198	−	0.714240i	0.108855	−	0.994058i	$-0.465282\pi$
$283$	−14.3194	−	12.0154i	−0.851198	−	0.714240i	−0.960053	+	0.279818i	$0.909726\pi$
$284$	8.75378	+	7.34530i	0.519441	+	0.435863i
$285$		0			0
$286$	−3.06864	−	1.11689i	−0.181453	−	0.0660434i
$287$	8.88709	−	15.3929i	0.524588	−	0.908614i
$288$		0			0
$289$	−11.1848	−	19.3726i	−0.657929	−	1.13957i
$290$	2.98055	+	16.9035i	0.175024	+	0.992610i
$291$		0			0
$292$	−16.1442	+	5.87600i	−0.944766	+	0.343867i
$293$	−1.87335	+	10.6243i	−0.109442	+	0.620677i	0.879911	+	0.475139i	$0.157602\pi$
$293$	−1.87335	+	10.6243i	−0.109442	+	0.620677i	−0.989353	+	0.145538i	$0.953509\pi$
$294$		0			0
$295$	−7.27926	+	6.10802i	−0.423815	+	0.355623i
$296$	14.6070			0.849017
$297$		0			0
$298$	7.02493			0.406943
$299$	−4.15158	+	3.48359i	−0.240092	+	0.201461i
$300$		0			0
$301$	−1.01506	+	5.75666i	−0.0585068	+	0.331809i
$302$	17.4598	−	6.35485i	1.00470	−	0.365680i
$303$		0			0
$304$	1.03163	+	5.85067i	0.0591681	+	0.335559i
$305$	0.406116	+	0.703413i	0.0232541	+	0.0402773i
$306$		0			0
$307$	−0.0248747	+	0.0430843i	−0.00141967	+	0.00245895i	−0.866734	−	0.498770i	$-0.833785\pi$
$307$	−0.0248747	+	0.0430843i	−0.00141967	+	0.00245895i	0.865315	+	0.501229i	$0.167119\pi$
$308$	10.3015	+	3.74943i	0.586981	+	0.213644i
$309$		0			0
$310$	4.00922	+	3.36413i	0.227708	+	0.191070i
$311$	10.1389	+	8.50759i	0.574927	+	0.482421i	0.883277	−	0.468852i	$-0.155332\pi$
$311$	10.1389	+	8.50759i	0.574927	+	0.482421i	−0.308350	+	0.951273i	$0.599777\pi$
$312$		0			0
$313$	14.1733	+	5.15866i	0.801123	+	0.291585i	0.709952	−	0.704250i	$-0.248717\pi$
$313$	14.1733	+	5.15866i	0.801123	+	0.291585i	0.0911710	+	0.995835i	$0.470939\pi$
$314$	1.05460	−	1.82662i	0.0595145	−	0.103082i
$315$		0			0
$316$	2.84656	+	4.93038i	0.160131	+	0.277356i
$317$	1.49873	+	8.49970i	0.0841769	+	0.477391i	0.997531	+	0.0702251i	$0.0223718\pi$
$317$	1.49873	+	8.49970i	0.0841769	+	0.477391i	−0.913354	+	0.407166i	$0.866517\pi$
$318$		0			0
$319$	27.4152	−	9.97831i	1.53496	−	0.558678i
$320$	−1.27074	+	7.20673i	−0.0710365	+	0.402868i
$321$		0			0
$322$	−6.04242	+	5.07019i	−0.336731	+	0.282551i
$323$	−50.6020			−2.81557
$324$		0			0
$325$	0.864837			0.0479725
$326$	13.1363	−	11.0226i	0.727551	−	0.610488i
$327$		0			0
$328$	3.25812	−	18.4777i	0.179900	−	1.02026i
$329$	10.8458	−	3.94755i	0.597949	−	0.217636i
$330$		0			0
$331$	5.38752	+	30.5541i	0.296125	+	1.67941i	0.662596	+	0.748977i	$0.269455\pi$
$331$	5.38752	+	30.5541i	0.296125	+	1.67941i	−0.366471	+	0.930430i	$0.619434\pi$
$332$	−0.637037	−	1.10338i	−0.0349619	−	0.0605559i
$333$		0			0
$334$	3.48067	−	6.02869i	0.190454	−	0.329875i
$335$	22.6048	+	8.22749i	1.23503	+	0.449516i
$336$		0			0
$337$	−18.2834	−	15.3416i	−0.995962	−	0.835711i	−0.00954207	−	0.999954i	$-0.503037\pi$
$337$	−18.2834	−	15.3416i	−0.995962	−	0.835711i	−0.986420	+	0.164243i	$0.947482\pi$
$338$	6.68070	+	5.60578i	0.363382	+	0.304914i
$339$		0			0
$340$	19.5475	+	7.11471i	1.06011	+	0.385850i
$341$	4.44790	−	7.70399i	0.240867	−	0.417194i
$342$		0			0
$343$	−9.68422	−	16.7736i	−0.522899	−	0.905688i
$344$	1.07151	+	6.07685i	0.0577721	+	0.327642i
$345$		0			0
$346$	1.92519	−	0.700711i	0.103499	−	0.0376704i
$347$	3.80485	−	21.5784i	0.204255	−	1.15839i	−0.694353	−	0.719634i	$-0.744309\pi$
$347$	3.80485	−	21.5784i	0.204255	−	1.15839i	0.898608	−	0.438752i	$-0.144580\pi$
$348$		0			0
$349$	12.1394	−	10.1862i	0.649807	−	0.545253i	−0.257205	−	0.966357i	$-0.582802\pi$
$349$	12.1394	−	10.1862i	0.649807	−	0.545253i	0.907012	+	0.421104i	$0.138357\pi$
$350$	1.25873			0.0672819
$351$		0			0
$352$	18.3894			0.980157
$353$	9.88725	−	8.29639i	0.526245	−	0.441572i	−0.340557	−	0.940224i	$-0.610616\pi$
$353$	9.88725	−	8.29639i	0.526245	−	0.441572i	0.866802	+	0.498652i	$0.166171\pi$
$354$		0			0
$355$	3.37992	−	19.1685i	0.179388	−	1.01736i
$356$	4.88837	−	1.77922i	0.259083	−	0.0942985i
$357$		0			0
$358$	−0.497603	−	2.82204i	−0.0262991	−	0.149150i
$359$	−12.9142	−	22.3681i	−0.681588	−	1.18054i	−0.974496	−	0.224404i	$-0.927956\pi$
$359$	−12.9142	−	22.3681i	−0.681588	−	1.18054i	0.292909	−	0.956140i	$-0.405377\pi$
$360$		0			0
$361$	−23.0196	+	39.8711i	−1.21156	+	2.09848i
$362$	−0.196234	−	0.0714235i	−0.0103138	−	0.00375393i
$363$		0			0
$364$	3.57322	+	2.99829i	0.187288	+	0.157153i
$365$	22.4171	+	18.8101i	1.17336	+	0.984568i
$366$		0			0
$367$	−15.0112	−	5.46363i	−0.783578	−	0.285199i	−0.0809141	−	0.996721i	$-0.525784\pi$
$367$	−15.0112	−	5.46363i	−0.783578	−	0.285199i	−0.702664	+	0.711522i	$0.748006\pi$
$368$	1.49343	−	2.58669i	0.0778503	−	0.134841i
$369$		0			0
$370$	−5.11194	−	8.85413i	−0.265757	−	0.460304i
$371$	0.0588538	+	0.333777i	0.00305554	+	0.0173288i
$372$		0			0
$373$	−1.71641	+	0.624722i	−0.0888724	+	0.0323469i	−0.386074	−	0.922468i	$-0.626169\pi$
$373$	−1.71641	+	0.624722i	−0.0888724	+	0.0323469i	0.297201	+	0.954815i	$0.403947\pi$
$374$	−2.66195	+	15.0967i	−0.137646	+	0.780630i
$375$		0			0
$376$	9.33336	−	7.83162i	0.481331	−	0.403885i
$377$	12.4136			0.639332
$378$		0			0
$379$	1.14694			0.0589141			0.0294571	−	0.999566i	$-0.490622\pi$
$379$	1.14694			0.0589141			0.0294571	+	0.999566i	$0.490622\pi$
$380$	20.4817	−	17.1862i	1.05069	−	0.881635i
$381$		0			0
$382$	0.323852	−	1.83666i	0.0165697	−	0.0939716i
$383$	−20.5112	+	7.46546i	−1.04807	+	0.381467i	−0.807935	−	0.589272i	$-0.799415\pi$
$383$	−20.5112	+	7.46546i	−1.04807	+	0.381467i	−0.240138	+	0.970739i	$0.577193\pi$
$384$		0			0
$385$	−3.24249	−	18.3891i	−0.165253	−	0.937194i
$386$	0.192957	+	0.334210i	0.00982123	+	0.0170109i
$387$		0			0
$388$	−4.18281	+	7.24484i	−0.212350	+	0.367801i
$389$	24.6164	+	8.95962i	1.24810	+	0.454271i	0.879759	−	0.475420i	$-0.157704\pi$
$389$	24.6164	+	8.95962i	1.24810	+	0.454271i	0.368340	+	0.929691i	$0.379926\pi$
$390$		0			0
$391$	19.4887	+	16.3529i	0.985584	+	0.827003i
$392$	−1.50313	−	1.26128i	−0.0759197	−	0.0637042i
$393$		0			0
$394$	−16.1855	−	5.89104i	−0.815414	−	0.296787i
$395$	4.84858	−	8.39798i	0.243958	−	0.422548i
$396$		0			0
$397$	−2.09915	−	3.63584i	−0.105353	−	0.182478i	0.808529	−	0.588456i	$-0.200264\pi$
$397$	−2.09915	−	3.63584i	−0.105353	−	0.182478i	−0.913883	+	0.405979i	$0.866931\pi$
$398$	−0.287994	−	1.63330i	−0.0144358	−	0.0818697i
$399$		0			0
$400$	−0.447894	+	0.163020i	−0.0223947	+	0.00815101i
$401$	−1.35963	+	7.71086i	−0.0678968	+	0.385062i	0.931856	+	0.362828i	$0.118189\pi$
$401$	−1.35963	+	7.71086i	−0.0678968	+	0.385062i	−0.999753	+	0.0222335i	$0.992922\pi$
$402$		0			0
$403$	2.89955	−	2.43301i	0.144437	−	0.121197i
$404$	14.2606			0.709493
$405$		0			0
$406$	18.0674			0.896669
$407$	−13.3122	+	11.1702i	−0.659859	+	0.553687i
$408$		0			0
$409$	−3.02651	+	17.1642i	−0.149651	+	0.848716i	0.813863	+	0.581057i	$0.197361\pi$
$409$	−3.02651	+	17.1642i	−0.149651	+	0.848716i	−0.963514	+	0.267658i	$0.913750\pi$
$410$	−12.3406	+	4.49161i	−0.609459	+	0.221825i
$411$		0			0
$412$	−2.06748	−	11.7253i	−0.101857	−	0.577662i
$413$	5.00118	+	8.66229i	0.246092	+	0.426243i
$414$		0			0
$415$	−1.08507	+	1.87940i	−0.0532642	+	0.0922563i
$416$	7.35266	+	2.67615i	0.360494	+	0.131209i
$417$		0			0
$418$	15.0935	+	12.6650i	0.738249	+	0.619464i
$419$	8.79662	+	7.38124i	0.429743	+	0.360597i	0.831855	−	0.554993i	$-0.187279\pi$
$419$	8.79662	+	7.38124i	0.429743	+	0.360597i	−0.402112	+	0.915591i	$0.631724\pi$
$420$		0			0
$421$	−6.85151	−	2.49375i	−0.333922	−	0.121538i	0.169617	−	0.985510i	$-0.445747\pi$
$421$	−6.85151	−	2.49375i	−0.333922	−	0.121538i	−0.503539	+	0.863972i	$0.667969\pi$
$422$	7.78066	−	13.4765i	0.378757	−	0.656026i
$423$		0			0
$424$	0.178889	+	0.309844i	0.00868759	+	0.0150474i
$425$	−0.704975	−	3.99811i	−0.0341963	−	0.193937i
$426$		0			0
$427$	0.803405	−	0.292416i	0.0388795	−	0.0141510i
$428$	−1.87632	+	10.6411i	−0.0906954	+	0.514359i
$429$		0			0
$430$	3.30853	−	2.77618i	0.159551	−	0.133879i
$431$	0.389084			0.0187415			0.00937075	−	0.999956i	$-0.497017\pi$
$431$	0.389084			0.0187415			0.00937075	+	0.999956i	$0.497017\pi$
$432$		0			0
$433$	24.1011			1.15822			0.579112	−	0.815248i	$-0.303400\pi$
$433$	24.1011			1.15822			0.579112	+	0.815248i	$0.303400\pi$
$434$	4.22016	−	3.54113i	0.202574	−	0.169980i
$435$		0			0
$436$	−0.303888	+	1.72344i	−0.0145536	+	0.0825376i
$437$	30.7271	−	11.1837i	1.46988	−	0.534991i
$438$		0			0
$439$	6.36691	+	36.1086i	0.303876	+	1.72337i	0.628748	+	0.777609i	$0.283568\pi$
$439$	6.36691	+	36.1086i	0.303876	+	1.72337i	−0.324871	+	0.945758i	$0.605321\pi$
$440$	−9.85567	−	17.0705i	−0.469851	−	0.813805i
$441$		0			0
$442$	−3.26131	+	5.64875i	−0.155125	+	0.268684i
$443$	35.5078	+	12.9238i	1.68703	+	0.614028i	0.994246	−	0.107118i	$-0.0341624\pi$
$443$	35.5078	+	12.9238i	1.68703	+	0.614028i	0.692782	+	0.721147i	$0.256385\pi$
$444$		0			0
$445$	−6.78776	−	5.69561i	−0.321771	−	0.269998i
$446$	7.91101	+	6.63813i	0.374597	+	0.314324i
$447$		0			0
$448$	7.23838	+	2.63456i	0.341981	+	0.124471i
$449$	−5.89289	+	10.2068i	−0.278103	+	0.481688i	−0.970913	−	0.239432i	$-0.923039\pi$
$449$	−5.89289	+	10.2068i	−0.278103	+	0.481688i	0.692811	+	0.721120i	$0.256372\pi$
$450$		0			0
$451$	11.1609	+	19.3313i	0.525547	+	0.910274i
$452$	−4.30276	−	24.4022i	−0.202385	−	1.14778i
$453$		0			0
$454$	−9.11412	+	3.31727i	−0.427747	+	0.155687i
$455$	1.37965	−	7.82441i	0.0646792	−	0.366814i
$456$		0			0
$457$	−15.2105	+	12.7631i	−0.711517	+	0.597034i	−0.925024	−	0.379908i	$-0.875956\pi$
$457$	−15.2105	+	12.7631i	−0.711517	+	0.597034i	0.213507	+	0.976942i	$0.431511\pi$
$458$	−19.9578			−0.932568
$459$		0			0
$460$	−13.4423			−0.626750
$461$	−5.85398	+	4.91207i	−0.272647	+	0.228778i	−0.768851	−	0.639428i	$-0.779171\pi$
$461$	−5.85398	+	4.91207i	−0.272647	+	0.228778i	0.496204	+	0.868206i	$0.334727\pi$
$462$		0			0
$463$	−2.77046	+	15.7120i	−0.128754	+	0.730200i	0.850253	+	0.526374i	$0.176449\pi$
$463$	−2.77046	+	15.7120i	−0.128754	+	0.730200i	−0.979007	+	0.203826i	$0.934662\pi$
$464$	−6.42893	+	2.33994i	−0.298455	+	0.108629i
$465$		0			0
$466$	0.728797	+	4.13321i	0.0337609	+	0.191467i
$467$	−13.0703	−	22.6385i	−0.604822	−	1.04758i	−0.992080	−	0.125611i	$-0.959911\pi$
$467$	−13.0703	−	22.6385i	−0.604822	−	1.04758i	0.387257	−	0.921972i	$-0.373423\pi$
$468$		0			0
$469$	12.6606	−	21.9288i	0.584613	−	1.01258i
$470$	−8.01351	−	2.91668i	−0.369636	−	0.134536i
$471$		0			0
$472$	8.08842	+	6.78699i	0.372300	+	0.312397i
$473$	−5.62359	−	4.71875i	−0.258573	−	0.216968i
$474$		0			0
$475$	−4.90339	−	1.78469i	−0.224983	−	0.0818871i
$476$	10.9483	−	18.9629i	0.501812	−	0.869164i
$477$		0			0
$478$	3.25522	+	5.63820i	0.148890	+	0.257885i
$479$	6.83310	+	38.7525i	0.312213	+	1.77065i	0.587442	+	0.809267i	$0.300135\pi$
$479$	6.83310	+	38.7525i	0.312213	+	1.77065i	−0.275229	+	0.961379i	$0.588754\pi$
$480$		0			0
$481$	−6.94820	+	2.52894i	−0.316811	+	0.115310i
$482$	0.0597185	−	0.338680i	0.00272010	−	0.0154265i
$483$		0			0
$484$	1.20958	−	1.01496i	0.0549811	−	0.0461346i
$485$	14.2493			0.647027
$486$		0			0
$487$	11.7133			0.530779			0.265389	−	0.964141i	$-0.414500\pi$
$487$	11.7133			0.530779			0.265389	+	0.964141i	$0.414500\pi$
$488$	0.691370	−	0.580128i	0.0312968	−	0.0262612i
$489$		0			0
$490$	−0.238488	+	1.35253i	−0.0107738	+	0.0611013i
$491$	36.2250	−	13.1848i	1.63481	−	0.595023i	0.648691	−	0.761052i	$-0.275317\pi$
$491$	36.2250	−	13.1848i	1.63481	−	0.595023i	0.986121	+	0.166030i	$0.0530947\pi$
$492$		0			0
$493$	−10.1190	−	57.3876i	−0.455736	−	2.58461i
$494$	4.19178	+	7.26038i	0.188597	+	0.326660i
$495$		0			0
$496$	−1.04304	+	1.80660i	−0.0468340	+	0.0811189i
$497$	−19.2527	−	7.00740i	−0.863601	−	0.314325i
$498$		0			0
$499$	−22.6455	−	19.0018i	−1.01375	−	0.850638i	−0.0249220	−	0.999689i	$-0.507934\pi$
$499$	−22.6455	−	19.0018i	−1.01375	−	0.850638i	−0.988830	+	0.149051i	$0.952378\pi$
$500$	−11.0552	−	9.27638i	−0.494402	−	0.414853i
$501$		0			0
$502$	12.4450	+	4.52959i	0.555445	+	0.202166i
$503$	−17.7888	+	30.8110i	−0.793161	+	1.37380i	0.130839	+	0.991404i	$0.458233\pi$
$503$	−17.7888	+	30.8110i	−0.793161	+	1.37380i	−0.924000	+	0.382392i	$0.875100\pi$
$504$		0			0
$505$	−12.1452	−	21.0361i	−0.540453	−	0.936092i
$506$	−1.72015	−	9.75548i	−0.0764702	−	0.433684i
$507$		0			0
$508$	−5.19886	+	1.89223i	−0.230662	+	0.0839541i
$509$	−4.92854	+	27.9512i	−0.218454	+	1.23891i	0.656358	+	0.754450i	$0.272096\pi$
$509$	−4.92854	+	27.9512i	−0.218454	+	1.23891i	−0.874812	+	0.484463i	$0.839015\pi$
$510$		0			0
$511$	23.5965	−	19.7998i	1.04385	−	0.875892i
$512$	−8.20265			−0.362510
$513$		0			0
$514$	−16.2365			−0.716161
$515$	−15.5353	+	13.0357i	−0.684567	+	0.574420i
$516$		0			0
$517$	−2.51702	+	14.2747i	−0.110698	+	0.627801i
$518$	−10.1128	+	3.68075i	−0.444330	+	0.161723i
$519$		0			0
$520$	−1.45639	−	8.25961i	−0.0638670	−	0.362208i
$521$	12.7176	+	22.0275i	0.557167	+	0.965041i	0.997731	+	0.0673204i	$0.0214450\pi$
$521$	12.7176	+	22.0275i	0.557167	+	0.965041i	−0.440565	+	0.897721i	$0.645222\pi$
$522$		0			0
$523$	−4.20395	+	7.28145i	−0.183826	+	0.318396i	−0.943180	−	0.332282i	$-0.892182\pi$
$523$	−4.20395	+	7.28145i	−0.183826	+	0.318396i	0.759354	+	0.650677i	$0.225515\pi$
$524$	0.134375	+	0.0489085i	0.00587020	+	0.00213658i
$525$		0			0
$526$	−11.5531	−	9.69416i	−0.503737	−	0.422686i
$527$	−13.6113	−	11.4212i	−0.592918	−	0.497517i
$528$		0			0
$529$	6.16460	+	2.24373i	0.268026	+	0.0975535i
$530$	0.125209	−	0.216868i	0.00543873	−	0.00942016i
$531$		0			0
$532$	−14.0719	−	24.3732i	−0.610093	−	1.05671i
$533$	1.64927	+	9.35348i	0.0714379	+	0.405144i
$534$		0			0
$535$	17.2949	−	6.29482i	0.747723	−	0.272149i
$536$	4.64155	−	26.3235i	0.200484	−	1.13700i
$537$		0			0
$538$	−11.1286	+	9.33801i	−0.479788	+	0.402590i
$539$	2.33440			0.100550
$540$		0			0
$541$	−12.8635			−0.553043			−0.276522	−	0.961008i	$-0.589182\pi$
$541$	−12.8635			−0.553043			−0.276522	+	0.961008i	$0.589182\pi$
$542$	−7.70806	+	6.46783i	−0.331090	+	0.277817i
$543$		0			0
$544$	6.37820	−	36.1726i	0.273463	−	1.55089i
$545$	2.80107	−	1.01951i	0.119985	−	0.0436708i
$546$		0			0
$547$	2.27340	+	12.8931i	0.0972034	+	0.551268i	0.994050	+	0.108926i	$0.0347411\pi$
$547$	2.27340	+	12.8931i	0.0972034	+	0.551268i	−0.896847	+	0.442342i	$0.854148\pi$
$548$	5.31514	+	9.20609i	0.227051	+	0.393265i
$549$		0			0
$550$	−0.790392	+	1.36900i	−0.0337024	+	0.0583743i
$551$	−70.3817	−	25.6168i	−2.99836	−	1.09131i
$552$		0			0
$553$	−7.81929	−	6.56116i	−0.332510	−	0.279009i
$554$	−6.22071	−	5.21980i	−0.264293	−	0.221768i
$555$		0			0
$556$	−13.6878	−	4.98193i	−0.580490	−	0.211281i
$557$	−2.29110	+	3.96830i	−0.0970769	+	0.168142i	−0.910474	−	0.413567i	$-0.864283\pi$
$557$	−2.29110	+	3.96830i	−0.0970769	+	0.168142i	0.813397	+	0.581710i	$0.197616\pi$
$558$		0			0
$559$	−1.56179	−	2.70509i	−0.0660565	−	0.114413i
$560$	0.760371	+	4.31228i	0.0321316	+	0.182227i
$561$		0			0
$562$	10.4843	−	3.81598i	0.442255	−	0.160968i
$563$	2.13308	−	12.0973i	0.0898986	−	0.509840i	−0.906293	−	0.422650i	$-0.861100\pi$
$563$	2.13308	−	12.0973i	0.0898986	−	0.509840i	0.996192	−	0.0871905i	$-0.0277889\pi$
$564$		0			0
$565$	−32.3315	+	27.1293i	−1.36020	+	1.14134i
$566$	14.5378			0.611071
$567$		0			0
$568$	−21.6278			−0.907484
$569$	11.1028	−	9.31634i	0.465453	−	0.390561i	−0.379680	−	0.925118i	$-0.623966\pi$
$569$	11.1028	−	9.31634i	0.465453	−	0.390561i	0.845133	+	0.534557i	$0.179521\pi$
$570$		0			0
$571$	−3.82814	+	21.7104i	−0.160203	+	0.908554i	0.793672	+	0.608346i	$0.208167\pi$
$571$	−3.82814	+	21.7104i	−0.160203	+	0.908554i	−0.953874	+	0.300207i	$0.902944\pi$
$572$	−5.50467	+	2.00354i	−0.230162	+	0.0837721i
$573$		0			0
$574$	2.40044	+	13.6135i	0.100192	+	0.568218i
$575$	1.31172	+	2.27197i	0.0547025	+	0.0947475i
$576$		0			0
$577$	15.7418	−	27.2655i	0.655338	−	1.13508i	−0.326471	−	0.945207i	$-0.605859\pi$
$577$	15.7418	−	27.2655i	0.655338	−	1.13508i	0.981809	−	0.189872i	$-0.0608072\pi$
$578$	16.3483	+	5.95031i	0.680001	+	0.247500i
$579$		0			0
$580$	23.5866	+	19.7915i	0.979380	+	0.821798i
$581$	1.74990	+	1.46834i	0.0725979	+	0.0609169i
$582$		0			0
$583$	−0.399973	−	0.145578i	−0.0165652	−	0.00602923i
$584$	16.2582	−	28.1600i	0.672768	−	1.16527i
$585$		0			0
$586$	−4.19516	−	7.26623i	−0.173300	−	0.300165i
$587$	−2.49523	−	14.1511i	−0.102989	−	0.584080i	−0.992004	−	0.126203i	$-0.959721\pi$
$587$	−2.49523	−	14.1511i	−0.102989	−	0.584080i	0.889015	−	0.457877i	$-0.151390\pi$
$588$		0			0
$589$	−21.4605	+	7.81097i	−0.884263	+	0.321845i
$590$	1.28332	−	7.27804i	0.0528333	−	0.299632i
$591$		0			0
$592$	3.12173	−	2.61944i	0.128302	−	0.107659i
$593$	−41.0988			−1.68772			−0.843862	−	0.536560i	$-0.819724\pi$
$593$	−41.0988			−1.68772			−0.843862	+	0.536560i	$0.819724\pi$
$594$		0			0
$595$	−37.2966			−1.52901
$596$	9.65342	−	8.10018i	0.395419	−	0.331796i
$597$		0			0
$598$	0.731913	−	4.15089i	0.0299301	−	0.169742i
$599$	−8.04580	+	2.92843i	−0.328742	+	0.119652i	−0.501118	−	0.865379i	$-0.667078\pi$
$599$	−8.04580	+	2.92843i	−0.328742	+	0.119652i	0.172376	+	0.985031i	$0.444856\pi$
$600$		0			0
$601$	−0.283951	−	1.61037i	−0.0115826	−	0.0656883i	0.978469	−	0.206396i	$-0.0661734\pi$
$601$	−0.283951	−	1.61037i	−0.0115826	−	0.0656883i	−0.990051	+	0.140707i	$0.955062\pi$
$602$	−2.27311	−	3.93713i	−0.0926449	−	0.160466i
$603$		0			0
$604$	16.6651	−	28.8648i	0.678094	−	1.17449i
$605$	−2.52733	−	0.919873i	−0.102751	−	0.0373982i
$606$		0			0
$607$	5.03248	+	4.22275i	0.204262	+	0.171396i	0.739180	−	0.673508i	$-0.235213\pi$
$607$	5.03248	+	4.22275i	0.204262	+	0.171396i	−0.534918	+	0.844904i	$0.679658\pi$
$608$	−36.1651	−	30.3461i	−1.46669	−	1.23070i
$609$		0			0
$610$	−0.593602	−	0.216054i	−0.0240343	−	0.00874775i
$611$	−3.08374	+	5.34120i	−0.124755	+	0.216082i
$612$		0			0
$613$	13.1363	+	22.7527i	0.530569	+	0.918973i	0.999364	+	0.0356656i	$0.0113551\pi$
$613$	13.1363	+	22.7527i	0.530569	+	0.918973i	−0.468795	+	0.883307i	$0.655312\pi$
$614$	−0.00671875	−	0.0381039i	−0.000271147	−	0.00153775i
$615$		0			0
$616$	−19.4971	+	7.09638i	−0.785562	+	0.285921i
$617$	−1.08930	+	6.17772i	−0.0438535	+	0.248706i	−0.998852	−	0.0479054i	$-0.984745\pi$
$617$	−1.08930	+	6.17772i	−0.0438535	+	0.248706i	0.954998	+	0.296611i	$0.0958565\pi$
$618$		0			0
$619$	3.78493	−	3.17593i	0.152129	−	0.127651i	−0.563546	−	0.826084i	$-0.690563\pi$
$619$	3.78493	−	3.17593i	0.152129	−	0.127651i	0.715676	+	0.698433i	$0.246119\pi$
$620$	9.38839			0.377047
$621$		0			0
$622$	−10.2936			−0.412738
$623$	−7.14489	+	5.99528i	−0.286254	+	0.240196i
$624$		0			0
$625$	−4.83028	+	27.3939i	−0.193211	+	1.09576i
$626$	−11.0230	+	4.01206i	−0.440569	+	0.160354i
$627$		0			0
$628$	−0.657012	−	3.72610i	−0.0262176	−	0.148688i
$629$	17.3550	+	30.0598i	0.691991	+	1.19856i
$630$		0			0
$631$	3.46210	−	5.99653i	0.137824	−	0.238718i	−0.788849	−	0.614587i	$-0.789322\pi$
$631$	3.46210	−	5.99653i	0.137824	−	0.238718i	0.926673	+	0.375869i	$0.122656\pi$
$632$	−10.1253	−	3.68530i	−0.402762	−	0.146593i
$633$		0			0
$634$	−5.14205	−	4.31469i	−0.204217	−	0.171358i
$635$	7.21889	+	6.05737i	0.286473	+	0.240379i
$636$		0			0
$637$	0.933370	+	0.339719i	0.0369815	+	0.0134601i
$638$	−11.3450	+	19.6502i	−0.449154	+	0.777957i
$639$		0			0
$640$	11.0653	+	19.1657i	0.437394	+	0.757589i
$641$	−5.88995	−	33.4036i	−0.232639	−	1.31936i	−0.847529	−	0.530749i	$-0.821911\pi$
$641$	−5.88995	−	33.4036i	−0.232639	−	1.31936i	0.614890	−	0.788613i	$-0.289200\pi$
$642$		0			0
$643$	−7.25745	+	2.64150i	−0.286206	+	0.104170i	−0.481134	−	0.876647i	$-0.659775\pi$
$643$	−7.25745	+	2.64150i	−0.286206	+	0.104170i	0.194928	+	0.980818i	$0.437553\pi$
$644$	−2.45704	+	13.9346i	−0.0968210	+	0.549099i
$645$		0			0
$646$	30.1476	−	25.2968i	1.18614	−	0.995289i
$647$	35.1862			1.38331			0.691655	−	0.722228i	$-0.256882\pi$
$647$	35.1862			1.38331			0.691655	+	0.722228i	$0.256882\pi$
$648$		0			0
$649$	−12.5615			−0.493083
$650$	−0.515251	+	0.432347i	−0.0202098	+	0.0169580i
$651$		0			0
$652$	5.34163	−	30.2939i	0.209194	−	1.18640i
$653$	−18.3353	+	6.67349i	−0.717514	+	0.261154i	−0.674870	−	0.737937i	$-0.735800\pi$
$653$	−18.3353	+	6.67349i	−0.717514	+	0.261154i	−0.0426440	+	0.999090i	$0.513578\pi$
$654$		0			0
$655$	−0.0422958	−	0.239871i	−0.00165263	−	0.00937255i
$656$	−2.61726	−	4.53323i	−0.102187	−	0.176993i
$657$		0			0
$658$	−4.48824	+	7.77386i	−0.174970	+	0.303057i
$659$	−21.6942	−	7.89603i	−0.845085	−	0.307586i	−0.117050	−	0.993126i	$-0.537344\pi$
$659$	−21.6942	−	7.89603i	−0.845085	−	0.307586i	−0.728035	+	0.685540i	$0.759566\pi$
$660$		0			0
$661$	−5.26760	−	4.42004i	−0.204886	−	0.171920i	0.534571	−	0.845123i	$-0.320473\pi$
$661$	−5.26760	−	4.42004i	−0.204886	−	0.171920i	−0.739457	+	0.673204i	$0.764918\pi$
$662$	−18.4843	−	15.5102i	−0.718412	−	0.602819i
$663$		0			0
$664$	2.26596	+	0.824741i	0.0879362	+	0.0320062i
$665$	−23.9688	+	41.5152i	−0.929471	+	1.60989i
$666$		0			0
$667$	18.8280	+	32.6110i	0.729023	+	1.26270i
$668$	−2.16844	−	12.2978i	−0.0838995	−	0.475818i
$669$		0			0
$670$	−17.5805	+	6.39879i	−0.679195	+	0.247207i
$671$	−0.186449	+	1.05740i	−0.00719777	+	0.0408206i
$672$		0			0
$673$	−23.4964	+	19.7158i	−0.905718	+	0.759988i	−0.971300	−	0.237859i	$-0.923554\pi$
$673$	−23.4964	+	19.7158i	−0.905718	+	0.759988i	0.0655815	+	0.997847i	$0.479110\pi$
$674$	18.5624			0.714997
$675$		0			0
$676$	15.6442			0.601700
$677$	−10.4059	+	8.73161i	−0.399932	+	0.335583i	−0.820467	−	0.571693i	$-0.806287\pi$
$677$	−10.4059	+	8.73161i	−0.399932	+	0.335583i	0.420535	+	0.907276i	$0.361842\pi$
$678$		0			0
$679$	2.60455	−	14.7711i	0.0999534	−	0.566864i
$680$	−36.9967	+	13.4657i	−1.41876	+	0.516386i
$681$		0			0
$682$	1.20139	+	6.81344i	0.0460037	+	0.260900i
$683$	3.03350	+	5.25418i	0.116074	+	0.201045i	0.918208	−	0.396098i	$-0.129636\pi$
$683$	3.03350	+	5.25418i	0.116074	+	0.201045i	−0.802135	+	0.597143i	$0.796302\pi$
$684$		0			0
$685$	9.05335	−	15.6809i	0.345911	−	0.599135i
$686$	14.1550	+	5.15201i	0.540442	+	0.196705i
$687$		0			0
$688$	1.31875	+	1.10656i	0.0502767	+	0.0421871i
$689$	−0.138736	−	0.116414i	−0.00528544	−	0.00443501i
$690$		0			0
$691$	−19.4188	−	7.06787i	−0.738727	−	0.268875i	−0.0548728	−	0.998493i	$-0.517475\pi$
$691$	−19.4188	−	7.06787i	−0.738727	−	0.268875i	−0.683854	+	0.729619i	$0.739698\pi$
$692$	1.83756	−	3.18275i	0.0698537	−	0.120990i
$693$		0			0
$694$	8.52054	+	14.7580i	0.323435	+	0.560206i
$695$	4.30835	+	24.4339i	0.163425	+	0.926830i
$696$		0			0
$697$	41.8964	−	15.2490i	1.58694	−	0.577599i
$698$	−2.14015	+	12.1374i	−0.0810058	+	0.459407i
$699$		0			0
$700$	1.72970	−	1.45139i	0.0653766	−	0.0548575i
$701$	11.0222			0.416303			0.208151	−	0.978097i	$-0.433255\pi$
$701$	11.0222			0.416303			0.208151	+	0.978097i	$0.433255\pi$
$702$		0			0
$703$	44.6131			1.68262
$704$	−7.41054	+	6.21818i	−0.279295	+	0.234356i
$705$		0			0
$706$	−1.74310	+	9.88560i	−0.0656024	+	0.372050i
$707$	−24.0264	+	8.74489i	−0.903605	+	0.328885i
$708$		0			0
$709$	−1.90795	−	10.8205i	−0.0716546	−	0.406373i	−0.999446	−	0.0332746i	$-0.989406\pi$
$709$	−1.90795	−	10.8205i	−0.0716546	−	0.406373i	0.927792	−	0.373099i	$-0.121705\pi$
$710$	7.56897	+	13.1098i	0.284058	+	0.492003i
$711$		0			0
$712$	−4.92288	+	8.52669i	−0.184493	+	0.319551i
$713$	10.7895	+	3.92704i	0.404068	+	0.147069i
$714$		0			0
$715$	7.64354	+	6.41369i	0.285852	+	0.239858i
$716$	−3.93778	−	3.30419i	−0.147162	−	0.123483i
$717$		0			0
$718$	18.8762	+	6.87038i	0.704454	+	0.256400i
$719$	−16.3529	+	28.3240i	−0.609859	+	1.05631i	0.381404	+	0.924408i	$0.375441\pi$
$719$	−16.3529	+	28.3240i	−0.609859	+	1.05631i	−0.991263	+	0.131898i	$0.957893\pi$
$720$		0			0
$721$	10.6734	+	18.4870i	0.397500	+	0.688490i
$722$	−6.21768	−	35.2622i	−0.231398	−	1.31232i
$723$		0			0
$724$	−0.352014	+	0.128123i	−0.0130825	+	0.00476164i
$725$	1.04347	−	5.91781i	0.0387535	−	0.219782i
$726$		0			0
$727$	29.4625	−	24.7220i	1.09271	−	0.916888i	0.0957920	−	0.995401i	$-0.469462\pi$
$727$	29.4625	−	24.7220i	1.09271	−	0.916888i	0.996913	+	0.0785129i	$0.0250172\pi$
$728$	−8.82830			−0.327199
$729$		0			0
$730$	−22.7591			−0.842352
$731$	−11.2325	+	9.42515i	−0.415447	+	0.348602i
$732$		0			0
$733$	2.44978	−	13.8934i	0.0904849	−	0.513165i	−0.905553	−	0.424233i	$-0.860544\pi$
$733$	2.44978	−	13.8934i	0.0904849	−	0.513165i	0.996038	−	0.0889317i	$-0.0283453\pi$
$734$	11.6747	−	4.24924i	0.430921	−	0.156842i
$735$		0			0
$736$	4.12160	+	23.3748i	0.151924	+	0.861605i
$737$	15.8999	+	27.5395i	0.585681	+	1.01443i
$738$		0			0
$739$	5.92286	−	10.2587i	0.217876	−	0.377372i	−0.736283	−	0.676674i	$-0.763421\pi$
$739$	5.92286	−	10.2587i	0.217876	−	0.377372i	0.954158	+	0.299302i	$0.0967539\pi$
$740$	−17.2340	−	6.27267i	−0.633535	−	0.230588i
$741$		0			0
$742$	−0.201924	−	0.169435i	−0.00741288	−	0.00622014i
$743$	−16.6749	−	13.9919i	−0.611743	−	0.513314i	0.283453	−	0.958986i	$-0.408520\pi$
$743$	−16.6749	−	13.9919i	−0.611743	−	0.513314i	−0.895196	+	0.445673i	$0.852965\pi$
$744$		0			0
$745$	−20.1701	−	7.34131i	−0.738974	−	0.268965i
$746$	0.710290	−	1.23026i	0.0260056	−	0.0450429i
$747$		0			0
$748$	13.7494	+	23.8147i	0.502729	+	0.870753i
$749$	−3.36412	−	19.0788i	−0.122922	−	0.697126i
$750$		0			0
$751$	39.9830	−	14.5526i	1.45900	−	0.531033i	0.513911	−	0.857844i	$-0.328196\pi$
$751$	39.9830	−	14.5526i	1.45900	−	0.531033i	0.945090	+	0.326811i	$0.105974\pi$
$752$	0.590247	−	3.34746i	0.0215241	−	0.122069i
$753$		0			0
$754$	−7.39574	+	6.20576i	−0.269337	+	0.226000i
$755$	−56.7719			−2.06614
$756$		0			0
$757$	−20.6382			−0.750110			−0.375055	−	0.927003i	$-0.622376\pi$
$757$	−20.6382			−0.750110			−0.375055	+	0.927003i	$0.622376\pi$
$758$	−0.683318	+	0.573372i	−0.0248192	+	0.0208258i
$759$		0			0
$760$	−8.78728	+	49.8352i	−0.318748	+	1.80771i
$761$	46.4631	−	16.9112i	1.68429	−	0.613030i	0.690400	−	0.723428i	$-0.257435\pi$
$761$	46.4631	−	16.9112i	1.68429	−	0.613030i	0.993887	+	0.110398i	$0.0352125\pi$
$762$		0			0
$763$	−0.544851	−	3.09000i	−0.0197249	−	0.111866i
$764$	−1.67275	−	2.89729i	−0.0605181	−	0.104820i
$765$		0			0
$766$	8.48799	−	14.7016i	0.306684	−	0.531192i
$767$	−5.02250	−	1.82804i	−0.181352	−	0.0660067i
$768$		0			0
$769$	16.9553	+	14.2272i	0.611424	+	0.513046i	0.895095	−	0.445876i	$-0.147108\pi$
$769$	16.9553	+	14.2272i	0.611424	+	0.513046i	−0.283670	+	0.958922i	$0.591552\pi$
$770$	11.1248	+	9.33482i	0.400910	+	0.336403i
$771$		0			0
$772$	0.650520	+	0.236770i	0.0234127	+	0.00852153i
$773$	−10.9836	+	19.0241i	−0.395051	+	0.684248i	−0.993108	−	0.117206i	$-0.962606\pi$
$773$	−10.9836	+	19.0241i	−0.395051	+	0.684248i	0.598057	+	0.801454i	$0.295940\pi$
$774$		0			0
$775$	−0.916134	−	1.58679i	−0.0329085	−	0.0569992i
$776$	−2.74941	−	15.5927i	−0.0986982	−	0.559745i
$777$		0			0
$778$	−19.1449	+	6.96819i	−0.686379	+	0.249822i
$779$	9.95104	−	56.4351i	0.356533	−	2.02200i
$780$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.595778 + 0.499917i) q^{2} +(-0.242262 + 1.37394i) q^{4} +(2.23304 - 0.812759i) q^{5} +(-0.434359 - 2.46337i) q^{7} +(-1.32025 - 2.28674i) q^{8} +O(q^{10})\)	\(q+(-0.595778 + 0.499917i) q^{2} +(-0.242262 + 1.37394i) q^{4} +(2.23304 - 0.812759i) q^{5} +(-0.434359 - 2.46337i) q^{7} +(-1.32025 - 2.28674i) q^{8} +(-0.924081 + 1.60056i) q^{10} +(2.95192 + 1.07441i) q^{11} +(1.02392 + 0.859169i) q^{13} +(1.49026 + 1.25048i) q^{14} +(-0.692233 - 0.251952i) q^{16} +(3.13726 - 5.43389i) q^{17} +(-4.03234 - 6.98422i) q^{19} +(0.575699 + 3.26495i) q^{20} +(-2.29581 + 0.835605i) q^{22} +(-0.704074 + 3.99300i) q^{23} +(0.495652 - 0.415902i) q^{25} -1.03954 q^{26} +3.48975 q^{28} +(7.11443 - 5.96971i) q^{29} +(0.491741 - 2.78880i) q^{31} +(5.50090 - 2.00216i) q^{32} +(0.847385 + 4.80576i) q^{34} +(-2.97207 - 5.14778i) q^{35} +(-2.76596 + 4.79078i) q^{37} +(5.89391 + 2.14521i) q^{38} +(-4.80674 - 4.03334i) q^{40} +(5.44333 + 4.56750i) q^{41} +(-2.19597 - 0.799267i) q^{43} +(-2.19131 + 3.79547i) q^{44} +(-1.57670 - 2.73092i) q^{46} +(0.801248 + 4.54411i) q^{47} +(0.698301 - 0.254161i) q^{49} +(-0.0873823 + 0.495570i) q^{50} +(-1.42850 + 1.19865i) q^{52} -0.135496 q^{53} +7.46499 q^{55} +(-5.05964 + 4.24554i) q^{56} +(-1.25426 + 7.11324i) q^{58} +(-3.75759 + 1.36765i) q^{59} +(0.0593526 + 0.336605i) q^{61} +(1.10120 + 1.90733i) q^{62} +(-1.53974 + 2.66690i) q^{64} +(2.98474 + 1.08636i) q^{65} +(7.75461 + 6.50689i) q^{67} +(6.70579 + 5.62682i) q^{68} +(4.34415 + 1.58114i) q^{70} +(4.09540 - 7.09344i) q^{71} +(6.15722 + 10.6646i) q^{73} +(-0.747095 - 4.23698i) q^{74} +(10.5728 - 3.84817i) q^{76} +(1.36448 - 7.73837i) q^{77} +(3.12600 - 2.62302i) q^{79} -1.75056 q^{80} -5.52638 q^{82} +(-0.699573 + 0.587012i) q^{83} +(2.58917 - 14.6839i) q^{85} +(1.70788 - 0.621616i) q^{86} +(-1.44038 - 8.16879i) q^{88} +(-1.86437 - 3.22919i) q^{89} +(1.67171 - 2.89548i) q^{91} +(-5.31556 - 1.93471i) q^{92} +(-2.74904 - 2.30672i) q^{94} +(-14.6809 - 12.3187i) q^{95} +(5.63467 + 2.05085i) q^{97} +(-0.288973 + 0.500515i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 6 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 6 * q^7 - 6 * q^8	\( 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 6 q^{10} + 15 q^{11} - 3 q^{13} + 21 q^{14} + 9 q^{16} + 9 q^{17} - 12 q^{19} + 3 q^{20} + 33 q^{22} - 15 q^{23} - 12 q^{25} + 48 q^{26} + 6 q^{28} + 6 q^{29} - 12 q^{31} + 27 q^{32} + 27 q^{34} - 30 q^{35} - 3 q^{37} + 39 q^{38} + 24 q^{40} + 39 q^{41} + 24 q^{43} + 33 q^{44} + 3 q^{46} + 42 q^{47} - 30 q^{49} + 15 q^{50} - 45 q^{52} - 18 q^{53} + 30 q^{55} - 12 q^{56} - 30 q^{58} - 15 q^{59} - 3 q^{61} + 30 q^{62} - 6 q^{64} + 6 q^{65} - 3 q^{67} - 36 q^{68} - 75 q^{70} - 12 q^{73} - 60 q^{74} + 30 q^{76} - 33 q^{77} + 33 q^{79} - 42 q^{80} - 42 q^{82} + 33 q^{83} - 18 q^{85} + 30 q^{86} - 42 q^{88} + 9 q^{89} - 18 q^{91} - 33 q^{92} - 66 q^{94} - 12 q^{95} + 15 q^{97} - 18 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 6 * q^10 + 15 * q^11 - 3 * q^13 + 21 * q^14 + 9 * q^16 + 9 * q^17 - 12 * q^19 + 3 * q^20 + 33 * q^22 - 15 * q^23 - 12 * q^25 + 48 * q^26 + 6 * q^28 + 6 * q^29 - 12 * q^31 + 27 * q^32 + 27 * q^34 - 30 * q^35 - 3 * q^37 + 39 * q^38 + 24 * q^40 + 39 * q^41 + 24 * q^43 + 33 * q^44 + 3 * q^46 + 42 * q^47 - 30 * q^49 + 15 * q^50 - 45 * q^52 - 18 * q^53 + 30 * q^55 - 12 * q^56 - 30 * q^58 - 15 * q^59 - 3 * q^61 + 30 * q^62 - 6 * q^64 + 6 * q^65 - 3 * q^67 - 36 * q^68 - 75 * q^70 - 12 * q^73 - 60 * q^74 + 30 * q^76 - 33 * q^77 + 33 * q^79 - 42 * q^80 - 42 * q^82 + 33 * q^83 - 18 * q^85 + 30 * q^86 - 42 * q^88 + 9 * q^89 - 18 * q^91 - 33 * q^92 - 66 * q^94 - 12 * q^95 + 15 * q^97 - 18 * q^98

Introduction

L-functions

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